Phonemicization of uvulars in Old IE?

I just had a nifty idea that I'm trying out. Bear with me. Again, this all refers back to my pdf containing my latest summary of theories of detailed chronology in Pre-IE so it might be interesting for any of you to take a gander who have not done so already: click here.

I'm doing another thought experiment here. Instinctively, I just can't let go of the idea that uvulars in PIE (Proto-Indo-European) were born at some point out of allophones of velars and that this allophony was initially triggered by neighbouring vowels. This is similar to what goes on in Khalkha (Mongolian). So in other words, *k when neighbouring a low vowel, *a, would once have yielded a uvular allophone /q/ (which is also phonetically speaking [+low]) while next to higher vowels, the more common /k/ would surface.

However, since I love simplicity and Occam's Razor so much, I wanted to see if I could cut it to the bare minimum and have this uvularization only possible in accented syllables in Mid IE. This almost explains everything since clusters like *kC- (i.e. phonetically /qC-/) are pretty rare in PIE. Unfortunately, they do occur nonetheless and, not only that, so do other well-established roots like *yeug- "to join" which imply pretty heavily that I'm wrong about uvularization only occuring in unaccented Mid IE (MIE) syllables since the corresponding MIE form of *yeug- could only have been *yéuCa- and yet a plain *g in place of this *C is insufficient to explain the later uvular we see in PIE. I've avoided this problem too long obviously so today's the day!

Ergo, if I'm correct that vowels triggered this uvularization in the first place and yet if I'm also correct that unaccented vowels merged into a single schwa by Mid IE, I'm forced to admit that uvulars must have already been phonemicized in the language by the time of contact with Proto-Semitic, circa 5500 BCE. Egad! I'll see where that idea takes me. It's just a titulating thought for now so forgive the mess.